What about the confessing Christian who lives like the world?
Fundamentally this is a question of misplaced confidence. So the first thing I do is try to determine why the person thinks he is a Christian. There are a variety of false objects of trust that could result in such a dichotomy: faith in a “decision,” family heritage, baptism, church attendance, etc. Then I take them to the words of Jesus in Mark 7:6-7 and show what Jesus thought of people who were confident that they knew God, but whose lives did not reflect such a relationship. According to Jesus, true faith is a matter of the heart, and not just the lips. Then I take such a person to Luke 6:43-49, where Jesus uses the picture of a fruit tree to show what he means by a heart that has placed its faith in him. Hearts are like trees, they produce fruit that everyone can see. Hearts are like fountains, they overflow in the words we speak. According to Jesus, the faith that trusts in him alone for forgiveness is also a faith that puts his words into practice. And so Jesus challenges our shallow confession of him as Lord. “Why do you call me ‘Lord, Lord’ and do not do what I say?” The day will come, Jesus warns in v. 49, when such a confession will prove to have been no confession of faith at all, and therefore provide no safety from the judgment of God.
I might also take such a person to 1 John 2:15-17, or James 4:4. Both warn against loving the world for the same reason: because we cannot love the world and God at the same time. We will either love one or the other, and ultimately we will follow the one we love.
I once counselled a woman who confessed to being a Christian, but who was sleeping with her boyfriend, even though she knew it was wrong. As we talked it became clear that though she gave lip service to following God, she was not prepared to follow God if it meant giving up what she admitted was an illicit sexual intimacy. She had come to me because she felt distant from God. The excitement and joy that had followed her initial commitment to Christ had dried up. After a series of meetings, in which I attempted to show her the biblical connection between true faith in Christ and its inevitable outworking in our lives, she broke off the discussion. She simply could not, would not, follow a God who would ask her to give up sex before marriage. No one can love God and the world at the same time.
Could I say, definitively, to that woman (or to anyone who confessed Christ but lived like the world) that she was not a Christian? No, for no one but God can read the human heart. What we can all read, however, is the fruit that the heart produces. And on that basis, I could give such a person no assurance or encouragement that she had found forgiveness of her sins in Jesus Christ. The free grace that forgives is also a grace that transforms, turning bad trees which produce bad fruit into good trees which produce good fruit. If our lives reflect this world, rather than God, then we must consider whether we have received the grace of God after all.
Further reading: John Piper, Desiring God.